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              <h1 id="一、Wolfram-Alpha介绍"><a href="#一、Wolfram-Alpha介绍" class="headerlink" title="一、Wolfram Alpha介绍"></a>一、Wolfram Alpha介绍</h1><p>Wolfram Alpha网址：<a href="https://www.wolframalpha.com/" target="_blank" rel="noopener">https://www.wolframalpha.com/</a></p>
<p>WolframAlpha是开发计算数学应用软件的沃尔夫勒姆研究公司开发出的新一代的搜索引擎，能根据问题直接给出答案的网站，用户在搜索框键入需要查询的问题后，该搜索引擎将直接向用户返回答案。</p>
<p>它是基于 Wolfram 早期旗舰产品 <a href="https://baike.baidu.com/item/Mathematica" target="_blank" rel="noopener">Mathematica</a>，一款囊括了计算机代数、符号和数值计算、可视化和统计功能的计算平台和工具包开发的。其数据来源包括学术网站和出版物、商业网站和公司、科学机构等等。</p>
<h1 id="二、计算微积分（图片版）"><a href="#二、计算微积分（图片版）" class="headerlink" title="二、计算微积分（图片版）"></a>二、计算微积分（图片版）</h1><p>那么怎么使用Wolfram Alpha来计算微积分呢？</p>
<p><img src= "/img/loading.gif" data-src="https://i.loli.net/2020/06/29/iRwNft9jPGu3Yna.gif" srcset="/img/loading.gif" alt=""></p>
<p><img src= "/img/loading.gif" data-src="https://i.loli.net/2020/06/29/QKNiA9V4lF5ehjH.gif" srcset="/img/loading.gif" alt="view_1_DGFPSw0wdoOatkCLh_ffwwmdwdHiFZTi3DpqnHqkJf0="></p>
<p><img src= "/img/loading.gif" data-src="https://i.loli.net/2020/06/29/U2xfBstVX7YnMzJ.gif" srcset="/img/loading.gif" alt="wKh2ClzcsvWAdBmEAAEWkzPRifs071"></p>
<p><img src= "/img/loading.gif" data-src="https://i.loli.net/2020/07/23/bOAtU8WTQGYXvxE.png" srcset="/img/loading.gif" alt="image008"></p>
<p>说明： 点击公式进入WolframAlpha网页，然后将其中的函数换成需要计算函数即可。</p>
<p><a href="http://www.wolfram.com/" target="_blank" rel="noopener">http://www.wolfram.com/</a></p>
<h1 id="三、计算微积分（表格版）"><a href="#三、计算微积分（表格版）" class="headerlink" title="三、计算微积分（表格版）"></a>三、计算微积分（表格版）</h1><table>
<thead>
<tr>
<th><strong>求极限</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=+lim+sin2x%2F(e^x-1)%2C+x->0" target="_blank" rel="noopener">lim sin2x/(e^x-1), x-&gt;0</a></th>
<th></th>
</tr>
</thead>
<tbody><tr>
<td><a href="http://www.wolframalpha.com/input/?i=lim+arctan(1%2Fx)+as+x->0%2B" target="_blank" rel="noopener">lim arctan(1/x) as x-&gt;0+</a>   <a href="http://www.wolframalpha.com/input/?i=+lim+exp(1%2Fx)+as+x->0-" target="_blank" rel="noopener">lim exp(1/x) as x-&gt;0-</a></td>
<td>单侧极限</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=lim+x^2sin(3%2Fx^2)" target="_blank" rel="noopener">lim x^2sin(3/x^2)) , x-&gt;oo</a>+%2C+x-&gt;oo)   <a href="http://www.wolframalpha.com/input/?i=lim+arctan(x)%2C+x->-oo" target="_blank" rel="noopener">lim arctan(x), x-&gt;-oo</a></td>
<td>x 趋于无穷大：oo</td>
<td></td>
</tr>
<tr>
<td><strong>求导数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=derivative+of+(2x^2%2B3)sin(x)" target="_blank" rel="noopener">derivative of (2x^2+3)sin(x)</a>   或  <a href="http://www.wolframalpha.com/input/?i=derivative+(2x^2%2B3)sin(x)" target="_blank" rel="noopener">derivative (2x^2+3)sin(x)</a></td>
<td>导数：derivative</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=d%2Fdx+(2x^2%2B3)sin(x)" target="_blank" rel="noopener">d/dx (2x^2+3)sin(x)</a></td>
<td>分式记号</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=((2x^2%2B3)sin(x))’" target="_blank" rel="noopener">((2x^2+3)sin(x))’</a></td>
<td>撇记号，最简单</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=derivative+of+(2x^2%2B3)sin(x)+at+x%3D3" target="_blank" rel="noopener">derivative of (2x^2+3)sin(x) at x=3</a></td>
<td>求一点的导数</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=d%2Fdx+(2x^2%2B3)sin(x)+at+x%3D3" target="_blank" rel="noopener">d/dx (2x^2+3)sin(x) at x=3</a></td>
<td></td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=((2x^2%2B3)sin(x))' target="_blank" rel="noopener"+at+x%3D3">((2x^2+3)sin(x))’ at x=3</a></td>
<td></td>
<td></td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>二阶导数</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=second+derivative+of+sin(2x^2%2B3)" target="_blank" rel="noopener">second derivative of sin(2x^2+3)</a></th>
<th>二阶导数：second derivative</th>
</tr>
</thead>
<tbody><tr>
<td><a href="http://www.wolframalpha.com/input/?i=2nd+derivative+sin(2x^2%2B3)" target="_blank" rel="noopener">2nd derivative sin(2x^2+3)</a></td>
<td></td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=(sin(2x^2%2B3))' target="_blank" rel="noopener"'">(sin(2x^2+3))’’</a></td>
<td>撇记号，最简单：打两撇</td>
<td></td>
</tr>
<tr>
<td><strong>三阶导数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=(sin(2x^2%2B3))' target="_blank" rel="noopener"''">(sin(2x^2+3))’’’</a></td>
<td>撇记号，最简单：打三撇</td>
</tr>
<tr>
<td><strong>10阶导数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=10th+derivative+1%2F(1%2Bx)" target="_blank" rel="noopener">10th derivative 1/(1+x)</a></td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=d^10%2Fdx^10(1%2F(1%2Bx))" target="_blank" rel="noopener">d^10/dx^10(1/(1+x))</a></td>
<td></td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=(exp(x)cos(2x^2))' target="_blank" rel="noopener"'+at+x%3D1">(exp(x)cos(2x^2))’’ at x=1</a></td>
<td>x=1处的2阶导数</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=7th+derivative+of+1%2F(1%2Bx)+at+0" target="_blank" rel="noopener">7th derivative of 1/(1+x) at 0</a></td>
<td>0处的7阶导数</td>
<td></td>
</tr>
<tr>
<td><strong>参数方程的导数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=+(sin(t))' target="_blank" rel="noopener"%2F(2t^2)'">(sin(t))’/(2t^2)’</a></td>
<td>x=2t^2, y=sint 的导数：dy/dx</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=(cost)' target="_blank" rel="noopener"%2F(sin2t)'+at+t%3Dpi%2F6">(cost)’/(sin2t)’ at t=pi/6</a></td>
<td>x=sin2t, y=cost 在 t=pi/6 处的导数</td>
<td></td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>隐函数的导数</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=-(+d%2Fdx(+1-x*exp(y)-y+)+)%2F(+d%2Fdy(+1-x*exp(y)-y+)+)" target="_blank" rel="noopener">-( d/dx( 1-x<em>exp(y)-y ) )/( d/dy( 1-x</em>exp(y)-y ) )</a></th>
<th>方程 y=1-xe^y 的导数:dy/dx</th>
</tr>
</thead>
<tbody><tr>
<td><strong>求方程的根</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=solve+x^3%2B1.1*x^2%2B0.9*x-1.4%3D0" target="_blank" rel="noopener">solve x^3+1.1<em>x^2+0.9</em>x-1.4=0</a></td>
<td>解方程求根（包括复根）</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=real+root+x^3%2B1.1*x^2%2B0.9*x-1.4%3D0" target="_blank" rel="noopener">real root x^3+1.1<em>x^2+0.9</em>x-1.4=0</a></td>
<td>只求实根(real root)</td>
<td></td>
</tr>
<tr>
<td><strong>求函数的驻点</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=stationary+point+of+x^3-2x%2B3" target="_blank" rel="noopener">stationary point of x^3-2x+3</a></td>
<td>驻点：stationary point</td>
</tr>
<tr>
<td><strong>求函数的极值</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=local+min+x%2F(x^2%2B2)" target="_blank" rel="noopener">local min x/(x^2+2)</a></td>
<td>极小值：local min</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=local+max+x%2F(x^2%2B2)" target="_blank" rel="noopener">local max x/(x^2+2)</a></td>
<td>极大值：local max</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=local+max+2sin(2x)^2-(5%2F2)cos(x%2F2)%2C+x%3D0+to+pi" target="_blank" rel="noopener">local max 2sin(2x)^2-(5/2)cos(x/2), x=0 to pi</a></td>
<td>求指定区间内的极大值</td>
<td></td>
</tr>
<tr>
<td><strong>求函数的最值</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=global+min+of+2sin(2x)^2-(5%2F2)cos(x%2F2)^2+for+1<%3Dx<%3D3" target="_blank" rel="noopener">global min of 2sin(2x)^2-(5/2)cos(x/2)^2 for 1&lt;=x&lt;=3</a></td>
<td>求指定区间内的最小值</td>
</tr>
<tr>
<td><strong>求曲线的拐点</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=inflection+point+of+x%2F(x^2%2B2)" target="_blank" rel="noopener">inflection point of x/(x^2+2)</a></td>
<td>拐点：inflection point</td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>求不定积分</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=integrate++x^2%2Bsin(x)%2B1" target="_blank" rel="noopener">integrate x^2+sin(x)+1</a></th>
<th>积分：integrate</th>
</tr>
</thead>
<tbody><tr>
<td><a href="http://www.wolframalpha.com/input/?i=int+xarctan(x)" target="_blank" rel="noopener">int xarctan(x)</a></td>
<td>int：integrate 的简写</td>
<td></td>
</tr>
<tr>
<td><strong>求定积分</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=integrate++x^2%2Bsin(x)%2B1+from+0+to+1+" target="_blank" rel="noopener">integrate x^2+sin(x)+1 from 0 to 1</a></td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=int++1%2Fsqrt(1-x^2)+%2C+x%3D+0+..1%2F2" target="_blank" rel="noopener">int 1/sqrt(1-x^2) , x= 0 ..1/2</a></td>
<td>简单的格式</td>
<td></td>
</tr>
<tr>
<td><strong>求广义积分</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=int++xexp(-2x)+from+0+to+oo" target="_blank" rel="noopener">int xexp(-2x) from 0 to oo</a></td>
<td>无穷大用两个o表示：oo</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=+int++1%2F(x^2%2B3)+%2C+x%3D+-oo+..+oo" target="_blank" rel="noopener">int 1/(x^2+3) , x= -oo .. oo</a></td>
<td></td>
<td></td>
</tr>
<tr>
<td><strong>求积分变限函数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=integrate+texp(-t)+from+0+to+x+" target="_blank" rel="noopener">integrate texp(-t) from 0 to x</a></td>
<td>积分上限函数</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=d%2Fdx+(+int+texp(-t)+from+0+to+x+)" target="_blank" rel="noopener">d/dx ( int texp(-t) from 0 to x )</a></td>
<td>积分上限函数求导</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=F(x)%3D%3Dintegrate+texp(-t)+from+ln(x)+to+x^2" target="_blank" rel="noopener">F(x)==integrate texp(-t) from ln(x) to x^2</a></td>
<td>积分变限函数</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=d%2Fdx+(integrate+texp(-t)+from+ln(x)+to+x^2+)" target="_blank" rel="noopener">d/dx (integrate texp(-t) from ln(x) to x^2 )</a></td>
<td>积分变限函数求导</td>
<td></td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>曲线与x轴之间的面积</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=area+between+2-x^2+and+x-axis" target="_blank" rel="noopener">area between 2-x^2 and x-axis</a></th>
<th>曲线y=2-x^2与x轴之间的面积</th>
</tr>
</thead>
<tbody><tr>
<td><strong>曲线下方的面积</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=area+under+3-x^2" target="_blank" rel="noopener">area under 3-x^2</a></td>
<td>曲线y=3-x^2与x轴之间的面积</td>
</tr>
<tr>
<td><strong>求两曲线之间的面积</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=area+between+x+and+x^2" target="_blank" rel="noopener">area between x and x^2</a></td>
<td>曲线y=x与y=x^2之间的面积</td>
</tr>
<tr>
<td>求两曲线的交点</td>
<td><a href="http://www.wolframalpha.com/input/?i=solve++x^2+%3D+x^3" target="_blank" rel="noopener">solve x^2 = x^3</a></td>
<td>曲线y=x^2与y=x^3的交点</td>
</tr>
<tr>
<td><strong>求两曲线之间的面积</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=area+between+sin(x)+and+cos(2x)+from+x%3D0+to+pi" target="_blank" rel="noopener">area between sin(x) and cos(2x) from x=0 to pi</a></td>
<td>曲线y=sinx与y=cos2x (0&lt;x&lt;pi) 之间的面积</td>
</tr>
<tr>
<td><strong>旋转体的体积</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=V%3Dpi*Integrate+(sin(x)^2%2C+x%3D0..2)" target="_blank" rel="noopener">V=pi*Integrate (sin(x)^2, x=0..2)</a></td>
<td>曲线y=sinx (0&lt;x&lt;2) 与x轴 之间的区域绕x轴旋转</td>
</tr>
<tr>
<td><strong>旋转体的体积</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=V%3Dpi*Integrate+(x^2-sin(x)^2%2C+x%3D0..pi)" target="_blank" rel="noopener">V=pi*Integrate (x^2-sin(x)^2, x=0..pi)</a></td>
<td>曲线y=x与y=sinx (0&lt;x&lt;pi) 之间的区域绕x轴旋转</td>
</tr>
<tr>
<td><strong>求曲线的弧长</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=int+sqrt(1%2B+(+(x^2)' target="_blank" rel="noopener"+)^2)%2C+x%3D1..3">int sqrt(1+ ( (x^2)’ )^2), x=1..3</a></td>
<td>曲线 y=x^2 (1&lt;x&lt;3) 的弧长</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=int++sqrt(+(sin(t^3))' target="_blank" rel="noopener"+^2%2B(t)'^2+)%2C+t%3D-1..1">int sqrt( (sin(t^3))’ ^2+(t)’^2 ), t=-1..1</a></td>
<td>参数曲线 x=sin(t^3), y=t (-1&lt;t&lt;1) 的弧长</td>
<td></td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>向量的点积</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=(1%2C2%2C4)+.+(-2%2C3%2C6)+" target="_blank" rel="noopener">(1,2,4) . (-2,3,6)</a></th>
<th></th>
</tr>
</thead>
<tbody><tr>
<td><strong>向量的叉积</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=+(1%2C2%2C4)+cross+(-2%2C3%2C6)" target="_blank" rel="noopener">(1,2,4) cross (-2,3,6)</a></td>
<td>叉积：cross</td>
</tr>
<tr>
<td><strong>求偏导数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=+d%2Fdx+sin(x^2%2B2y)" target="_blank" rel="noopener">d/dx sin(x^2+2y)</a></td>
<td>对 x 求偏导数</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=d%2Fdy+sin(x^2%2B2y)" target="_blank" rel="noopener">d/dy sin(x^2+2y)</a></td>
<td>对 y 求偏导数</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=d%2Fdx+sin(x^2%2B2y)+at+(1%2C2)" target="_blank" rel="noopener">d/dx sin(x^2+2y) at (1,2)</a></td>
<td>在某一点的偏导数</td>
<td></td>
</tr>
<tr>
<td><strong>高阶偏导数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=d%2Fdx+d%2Fdx+x^3*y^2+-+3*x*y^3+-+x*y+%2B+1" target="_blank" rel="noopener">d/dx d/dx x^3<em>y^2 - 3</em>x<em>y^3 - x</em>y + 1</a></td>
<td>对 x 的二阶偏导数</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=d%2Fdy+d%2Fdx+x^3*y^2+-+3*x*y^3+-+x*y+%2B+1" target="_blank" rel="noopener">d/dy d/dx x^3<em>y^2 - 3</em>x<em>y^3 - x</em>y + 1</a></td>
<td>混合偏导数</td>
<td></td>
</tr>
<tr>
<td><strong>隐函数的偏导数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=-(+d%2Fdx(+exp(z)-xyz+)+)%2F(+d%2Fdz+(exp(z)-xyz)+)" target="_blank" rel="noopener">-( d/dx( exp(z)-xyz ) )/( d/dz (exp(z)-xyz) )</a></td>
<td>方程e^z=xyz的偏导数：dz/dx</td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>向量函数的导数</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=(t^2%2C+4t-3%2C+2t^2-6t)' target="_blank" rel="noopener"">(t^2, 4t-3, 2t^2-6t)’</a></th>
<th>速度</th>
</tr>
</thead>
<tbody><tr>
<td><strong>向量函数的二阶导数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=(t^2%2C+e^t%2C+2t^3)' target="_blank" rel="noopener"'">(t^2, e^t, 2t^3)’’</a></td>
<td>加速度</td>
</tr>
<tr>
<td><strong>求梯度</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=grad++x^2%2Bcos(2y)+" target="_blank" rel="noopener">grad x^2+cos(2y) </a></td>
<td>二元函数的梯度</td>
</tr>
<tr>
<td>用 grad 或 del 求梯度</td>
<td><a href="http://www.wolframalpha.com/input/?i=del++x^2y%2Bcos(xy)%2Bxyz^2" target="_blank" rel="noopener">del x^2y+cos(xy)+xyz^2</a></td>
<td>三元函数的梯度</td>
</tr>
<tr>
<td><strong>求方向导数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=+derivative+of+x^2%2Bcos(2y)+in+the+direction+(2%2C-3)+at+(1%2C2)" target="_blank" rel="noopener">derivative of x^2+cos(2y) in the direction (2,-3) at (1,2)</a></td>
<td></td>
</tr>
<tr>
<td><strong>求二元函数的驻点</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=stationary+point+of++x^3-y^3%2B3*x^2%2B3*y^2-9*x" target="_blank" rel="noopener">stationary point of x^3-y^3+3<em>x^2+3</em>y^2-9*x</a></td>
<td>驻点：stationary point</td>
</tr>
<tr>
<td><strong>求二元函数的极值</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=local+max++x^3-y^3%2B3*x^2%2B3*y^2-9*x" target="_blank" rel="noopener">local max x^3-y^3+3<em>x^2+3</em>y^2-9*x</a></td>
<td>极大值：local max</td>
</tr>
<tr>
<td>或 <a href="http://www.wolframalpha.com/input/?i=+maximize++x^3-y^3%2B3*x^2%2B3*y^2-9*x" target="_blank" rel="noopener">maximize x^3-y^3+3<em>x^2+3</em>y^2-9*x</a></td>
<td>最大化：maximize</td>
<td></td>
</tr>
<tr>
<td><strong>求二元函数的最值</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=minimize+2(xy%2B2%2Fx%2B2%2Fy)++for+x>0%2C+y>0" target="_blank" rel="noopener">minimize 2(xy+2/x+2/y) for x&gt;0, y&gt;0</a></td>
<td>最小化：minimize</td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>求条件极值</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=maximize+xy+on+x%2By%3D1" target="_blank" rel="noopener">maximize xy on x+y=1</a></th>
<th>求函数xy在x+y=1上的最大值</th>
</tr>
</thead>
<tbody><tr>
<td><a href="http://www.wolframalpha.com/input/?i=maximize++xyz+on++2*(x*y+%2B+y*z+%2B+z*x)+%3D1%2C+x>0%2Cy>0%2Cz>0+" target="_blank" rel="noopener">maximize xyz on 2<em>(x</em>y + y<em>z + z</em>x) =1, x&gt;0,y&gt;0,z&gt;0</a></td>
<td></td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=maximize+sqrt(x^2%2By^2%2Bz^2)+on+z%3Dx^2%2By^2+and+x%2By%2Bz%3D1" target="_blank" rel="noopener">maximize sqrt(x^2+y^2+z^2) on z=x^2+y^2 and x+y+z=1</a></td>
<td>两个约束条件</td>
<td></td>
</tr>
<tr>
<td><strong>二重积分</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=int++x^2y%2Bx%2C++y%3D2..4%2C+x%3D1..3" target="_blank" rel="noopener">int x^2y+x, y=2..4, x=1..3</a></td>
<td>矩形区域</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=int++xy+%2C+x%3D1..2%2C+y%3D1..x" target="_blank" rel="noopener">int xy , x=1..2, y=1..x</a></td>
<td>先y, 后x</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=int++xy+%2C+y%3D-1..2%2C+x%3Dy^2..y%2B2" target="_blank" rel="noopener">int xy , y=-1..2, x=y^2..y+2</a></td>
<td>先x, 后y</td>
<td></td>
</tr>
<tr>
<td><strong>三重积分</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=int++x+%2C+x%3D0..1%2C+y%3D0..(1-x)%2F2%2C+z%3D0..1-x-2y" target="_blank" rel="noopener">int x , x=0..1, y=0..(1-x)/2, z=0..1-x-2y</a></td>
<td>积分次序:：z, y,x</td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>级数求和</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=sum+3*(2%2F5)^n%2C+n%3D1..oo" target="_blank" rel="noopener">sum 3*(2/5)^n, n=1..oo</a></th>
<th>等比级数求和</th>
</tr>
</thead>
<tbody><tr>
<td>用 sum 求和</td>
<td><a href="http://www.wolframalpha.com/input/?i=sum+1%2Fn^2%2C+n%3D1..oo" target="_blank" rel="noopener">sum 1/n^2, n=1..oo</a></td>
<td>p-级数求和</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=sum+(-1)^(n%2B1)%2Fn^2%2C+n%3D1..oo" target="_blank" rel="noopener">sum (-1)^(n+1)/n^2, n=1..oo</a></td>
<td>交错级数求和</td>
<td></td>
</tr>
<tr>
<td><strong>幂级数的和函数</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=sum+(-1)^(n%2B1)*x^(2n-1)%2F(2n-1)%2Cn%3D1...oo" target="_blank" rel="noopener">sum (-1)^(n+1)*x^(2n-1)/(2n-1),n=1…oo</a></td>
<td></td>
</tr>
<tr>
<td><strong>函数的泰勒公式</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=series+xsin(x)+to+order+5" target="_blank" rel="noopener">series xsin(x) to order 5</a>      series：级数</td>
<td>xsinx在x=0处的5阶泰勒公式</td>
</tr>
<tr>
<td>用series 或 taylor</td>
<td><a href="http://www.wolframalpha.com/input/?i=+taylor+e^x+at+x%3D1+to+order+5" target="_blank" rel="noopener">taylor e^x at x=1 to order 5</a>   taylor：泰勒</td>
<td>e^x在x=1处的5阶泰勒公式</td>
</tr>
<tr>
<td><strong>解微分方程</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=+y’%3D2xy" target="_blank" rel="noopener">y’=2xy</a></td>
<td>直接输入微分方程</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=y’%3De^(2x-y)%2C+y(0)%3D0" target="_blank" rel="noopener">y’=e^(2x-y), y(0)=0</a></td>
<td>求特解</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=(1%2Bx^2)y’’%3D2xy’%2C+y(0)%3D1%2C+y’(0)%3D3" target="_blank" rel="noopener">(1+x^2)y’’=2xy’, y(0)=1, y’(0)=3</a></td>
<td>二阶微分方程的特解</td>
<td></td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>高阶线性微分方程</strong></th>
<th><a href="http://www.wolframalpha.com/input/?i=y’’-5y’%2B6y%3Dxe^(2x)" target="_blank" rel="noopener">y’’-5y’+6y=xe^(2x)</a></th>
<th>二阶微分方程的通解</th>
</tr>
</thead>
<tbody><tr>
<td><a href="http://www.wolframalpha.com/input/?i=+y’’%2By%2Bsin(2x)%3D0%2C+y(pi)%3D1%2C+y’(pi)%3D1" target="_blank" rel="noopener">y’’+y+sin(2x)=0, y(pi)=1, y’(pi)=1</a></td>
<td>二阶微分方程的特解</td>
<td></td>
</tr>
<tr>
<td><strong>作 图</strong></td>
<td><img src= "/img/loading.gif" data-src="http://b.bst.126.net/common/portrait/face/preview/face1.gif" srcset="/img/loading.gif" alt="WolframAlpha 快速指南 - calculus - 高等数学"></td>
<td></td>
</tr>
<tr>
<td><strong>一元函数图形</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=+plot+y%3Dx^3-x^2-x%2B1%2C+x%3D-2..2" target="_blank" rel="noopener">plot y=x^3-x^2-x+1, x=-2..2</a></td>
<td>作图：plot</td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=plot+xsinx%2Carctanx" target="_blank" rel="noopener">plot xsinx,arctanx</a></td>
<td>两条曲线</td>
<td></td>
</tr>
<tr>
<td><strong>隐函数的图形</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=plot+x^3%2By^3%3D6xy" target="_blank" rel="noopener">plot x^3+y^3=6xy</a></td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=plot+x^3%2By^3%3D6xy%2C+x%3D-4..4%2C+y%3D-4..4" target="_blank" rel="noopener">plot x^3+y^3=6xy, x=-4..4, y=-4..4</a></td>
<td>指定范围</td>
<td></td>
</tr>
<tr>
<td><a href="http://www.wolframalpha.com/input/?i=+plot+x^2%2By^2%3D2x%2C+x%3Dy^3%2B1" target="_blank" rel="noopener">plot x^2+y^2=2x, x=y^3+1</a></td>
<td>两条曲线</td>
<td></td>
</tr>
<tr>
<td><strong>参数曲线</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=parametric+plot+(t(1-sint)%2Ctcost)+from+t%3D-10+to+10" target="_blank" rel="noopener">parametric plot (t(1-sint),tcost) from t=-10 to 10</a> parametric plot : 参数方程作图</td>
<td>参数方程 x=t(1-sint), y=tcost 的图形</td>
</tr>
<tr>
<td><strong>极坐标曲线</strong></td>
<td><a href="http://www.wolframalpha.com/input/?i=polar+plot+1%2Bcost%2C+t%3D0..2pi" target="_blank" rel="noopener">polar plot 1+cost, t=0..2pi</a>  polar plot: 极坐标作图</td>
<td>极坐标方程 r=1+cost 的图形</td>
</tr>
</tbody></table>
<table>
<thead>
<tr>
<th><strong>曲面作图</strong></th>
<th>[plot x^2+y^2, -2</th>
</tr>
</thead>
<tbody><tr>
<td><a href="http://www.wolframalpha.com/input/?i=plot++sqrt(2-x^2-3y^2)" target="_blank" rel="noopener">plot sqrt(2-x^2-3y^2)</a></td>
<td></td>
</tr>
</tbody></table>

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